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Block #284,842

2CCLength 9β˜…β˜†β˜†β˜†β˜†

Cunningham Chain of the Second Kind Β· Discovered 11/30/2013, 6:54:18 AM Β· Difficulty 9.9834 Β· 6,546,660 confirmations

2CC
Cunningham Chain of the Second Kind

A sequence where each prime is double the previous prime minus one.

Block Header
Block Hash
1a3808fcb9cc5e37d072319a629e94d781e835569728aa387bdc9b82b1fa32b4
View on Chainz β†—

Height

#284,842

Difficulty

9.983353

Transactions

1

Size

200 B

Version

2

Bits

09fbbd0a

Nonce

63,042

Timestamp

11/30/2013, 6:54:18 AM

Confirmations

6,546,660

Merkle Root

657321791e49117383b80536e76fa52961abf213bec9b9014af24a3b1a77d3f1
Transactions (1)
Coinbase657321791e4911…f24a3b1a77d3f1
1 in β†’ 1 out10.0200 XPM110 B
AeKNrjNj…1NEq95Ta
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.150 Γ— 10⁹⁡(96-digit number)
21508436768644213951…15946191528382365780
Discovered Prime Numbers
p_k = 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin + 1
2.150 Γ— 10⁹⁡(96-digit number)
21508436768644213951…15946191528382365781
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
2
2^1 Γ— origin + 1
4.301 Γ— 10⁹⁡(96-digit number)
43016873537288427903…31892383056764731561
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
3
2^2 Γ— origin + 1
8.603 Γ— 10⁹⁡(96-digit number)
86033747074576855807…63784766113529463121
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
4
2^3 Γ— origin + 1
1.720 Γ— 10⁹⁢(97-digit number)
17206749414915371161…27569532227058926241
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
5
2^4 Γ— origin + 1
3.441 Γ— 10⁹⁢(97-digit number)
34413498829830742322…55139064454117852481
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
6
2^5 Γ— origin + 1
6.882 Γ— 10⁹⁢(97-digit number)
68826997659661484645…10278128908235704961
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
7
2^6 Γ— origin + 1
1.376 Γ— 10⁹⁷(98-digit number)
13765399531932296929…20556257816471409921
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
8
2^7 Γ— origin + 1
2.753 Γ— 10⁹⁷(98-digit number)
27530799063864593858…41112515632942819841
Verify on FactorDB β†—Wolfram Alpha β†—
Γ—2βˆ’1 β†’
9
2^8 Γ— origin + 1
5.506 Γ— 10⁹⁷(98-digit number)
55061598127729187716…82225031265885639681
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 consecutive prime numbers forming a Cunningham Chain of the Second Kind. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

View full Prime Chain Discovery page β†’
β˜…β˜†β˜†β˜†β˜†
Rarity
CommonChain length 9
How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the 2CC formula:

2CC: p₁ (first prime), pβ‚‚ = 2p₁ βˆ’ 1, p₃ = 2pβ‚‚ βˆ’ 1, …
Verify on a Primecoin Node

Anyone running a Primecoin node can independently verify this block using the following RPC commands. Run these from the primecoin-cli command line or via the debug console in the Primecoin wallet.

1. Get block hash by height
getblockhash 284842

Returns the block hash for a given block height. Use this to confirm the hash shown above matches the chain.

2. Get full block data
getblock 1a3808fcb9cc5e37d072319a629e94d781e835569728aa387bdc9b82b1fa32b4

Returns the full block header including difficulty, prime chain origin, prime chain type, transaction IDs, and all other fields shown on this page.

How to run these commands: To verify this data independently, open a terminal on your own Primecoin node and run primecoin-cli <command>. Alternatively, open the Primecoin-Qt wallet, go to Help β†’ Debug Window β†’ Console, and type the command directly. The node must be fully synced to this block height for the commands to return results.

Cross-reference on Chainz Explorer

Chainz is an independent Primecoin block explorer. Compare this block's data to verify accuracy.

View Block #284,842 on Chainz β†—
Circulating Supply:57,896,104 XPMΒ·at block #6,831,501 Β· updates every 60s
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